Cluster states of two photons and four qubits, built on the double entanglement of two photons in the degrees
of freedom of polarization and linear momentum, have been used in the realization of a complete set of basic
operations of one-way quantum computation. Basic computation algorithms, namely, the Grover's search and
the Deutsch's algorithm, have been realized by using these states. Hyperentangled states of increasing size are
of paramount importance for the realization of even more complex algorithms and can be extended to a lager
number of degrees of freedom of the photons. Some recent results obtained with entangled states of two photons
and six qubits are presented.